from tools import number_theory

def test_prime(x, prime):
    for p in prime:
        if p ** 2 > x:
            return True
        if not (x % p):
            return False
    return False

def gen_value(a, b):
    n = 0
    x = b
    prime = list(number_theory.make_prime(10000))
    while True:
        if prime[-1] ** 2 < x:
            prime = list(number_theory.make_prime(prime[-1] * 2 + 1))
        if 0 > x:
            return
        if not test_prime(x, prime):
            return
        yield x
        x += 2 * n + a + 1
        n += 1        

def test_polynomial(limit):
    maxi = [0, (0, 0)]
    for b in number_theory.make_prime(limit):
        for a in range(-b, 0, 2):
            l = len(list(gen_value(a, b)))
            if l > maxi[0]:
                maxi = [l, (a, b)]
                print(maxi)
    return maxi[1][0] * maxi[1][1]

print(test_polynomial(1000))